Finite Group Databasebeta

← C113×#9113 #43277133

Subgroups — C113×#9113 #43277133

Order 28928.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C113C211yesmaximal, characteristic, complemented
2C113×#2847C211yesmaximal, characteristic
3C2×#327×C113C212yesmaximal, complemented
4C113×C22⋊#95C211yesmaximal, characteristic, complemented
5C113×#1294C212yesmaximal, complemented
6C24×C4×C113C2211yescharacteristic
7C23×C8×C113—21no—
8C2×#121×C113C411yescharacteristic, complemented
9C2×#121×C113C411yescharacteristic, complemented
10C2×#121×C113C2211yescharacteristic
11C2×#120×C113—21no—
12C22×C22⋊C4×C113—21no—
13C2×C22⋊C8×C113—21no—
14C2×C22⋊C8×C113—24no—
15C2×C22⋊C8×C113C2212yes—
16#386×C113—21no—
17#386×C113—21no—
18#386×C113—21no—
19#380×C113C411yescharacteristic, complemented
20#380×C113C411yescharacteristic, complemented
21#380×C113C2211yescharacteristic
22C2×#95×C113—21no—
23C2×#95×C113C2212yes—
24#327×C113—24no—
25C25×C113D411yescharacteristic
26C22×D4×C113—21no—
27C22×D4×C113—21no—
28C22×D4×C113—21no—
29C22×D4×C113C2×C411yescharacteristic
30C23×C4×C113—22no—
31C23×C4×C113—22no—
32C23×C4×C113—22no—
33C23×C4×C113—42no—
34C23×C4×C113—42no—
35C23×C4×C113C2×C411yescharacteristic
36C23×C4×C113C2×C411yescharacteristic
37C23×C4×C113D411yescharacteristic
38C23×C4×C113D411yescharacteristic
39C23×C4×C113D411yescharacteristic
40C23×C4×C113C2311yescharacteristic
41C22×C8×C113—24no—
42C22×C8×C113—22no—
43C22×C8×C113—42no—
44C22×C8×C113—42no—
45#121×C113—22no—
46#121×C113—22no—
47#121×C113—42no—
48#121×C113—42no—
49#120×C113—42no—
50#120×C113—42no—
51C2×C4⋊C4×C113C2×C411yescharacteristic
52C2×C4⋊C4×C113C2×C411yescharacteristic
53C2×C4⋊C4×C113C2×C411yescharacteristic
54C2×C22⋊C4×C113—24no—
55C2×C22⋊C4×C113—21no—
56C2×C22⋊C4×C113—21no—
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—21no—
59C2×C22⋊C4×C113—21no—
60C2×C22⋊C4×C113—21no—
61C2×C22⋊C4×C113—42no—
62C2×C22⋊C4×C113—42no—
63C22⋊C8×C113—24no—
64C22⋊C8×C113—22no—
65C22⋊C8×C113D414yescomplemented
66#95×C113—21no—
67#95×C113—21no—
68#95×C113—21no—
69#95×C113—22no—
70#95×C113—22no—
71#95×C113—42no—
72C24×C113—22no—
73C24×C113—22no—
74C24×C113—22no—
75C24×C113—22no—
76C24×C113—21no—
77C24×C113—41no—
78C24×C113—41no—
79C24×C113C22⋊C411yescharacteristic
80C24×C113C22⋊C411yescharacteristic
81C24×C113D812yes—
82C24×C113SD1612yes—
83C24×C113C2×D411yescharacteristic
84C2×D4×C113—22no—
85C2×D4×C113—41no—
86C2×D4×C113—41no—
87C2×D4×C113—42no—
88C2×D4×C113—42no—
89C2×D4×C113—42no—
90C2×D4×C113—42no—
91C2×D4×C113—42no—
92C2×D4×C113—42no—
93C2×D4×C113—42no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—42no—
97C22×C4×C113—22no—
98C22×C4×C113—22no—
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—22no—
102C22×C4×C113—22no—
103C22×C4×C113—22no—
104C22×C4×C113—22no—
105C22×C4×C113—22no—
106C22×C4×C113—22no—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113—24no—
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113—21no—
113C22×C4×C113—41no—
114C22×C4×C113—41no—
115C22×C4×C113—41no—
116C22×C4×C113—41no—
117C22×C4×C113—41no—
118C22×C4×C113—41no—
119C22×C4×C113—41no—
120C22×C4×C113—48no—
121C22×C4×C113—48no—
122C22×C4×C113—42no—
123C22×C4×C113—42no—
124C22×C4×C113—42no—
125C22×C4×C113—42no—
126C22×C4×C113—42no—
127C22×C4×C113—42no—
128C22×C4×C113C22⋊C411yescharacteristic
129C22×C4×C113C22⋊C411yescharacteristic
130C22×C4×C113C22×C411yescharacteristic
131C22×C4×C113C2×D411yescharacteristic
132C22×C4×C113C2×D412yes—
133C22×C4×C113#4112yes—
134C2×C8×C113—24no—
135C2×C8×C113—48no—
136C2×C8×C113—42no—
137C2×C8×C113—42no—
138C4⋊C4×C113—22no—
139C4⋊C4×C113—41no—
140C4⋊C4×C113—41no—
141C22⋊C4×C113—42no—
142C22⋊C4×C113—48no—
143C22⋊C4×C113—42no—
144C22⋊C4×C113—42no—
145C22⋊C4×C113—41no—
146C22⋊C4×C113—41no—
147C22⋊C4×C113—42no—
148C22⋊C4×C113—41no—
149C22⋊C4×C113—41no—
150C23×C113—21no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—21no—
154C23×C113—21no—
155C23×C113—21no—
156C23×C113—21no—
157C23×C113—21no—
158C23×C113—24no—
159C23×C113—24no—
160C23×C113—21no—
161C23×C113—21no—
162C23×C113—21no—
163C23×C113—21no—
164C23×C113—21no—
165C23×C113—21no—
166C23×C113—24no—
167C23×C113—24no—
168C23×C113—42no—
169C23×C113—42no—
170C23×C113—44no—
171C23×C113—44no—
172C23×C113—44no—
173C23×C113—44no—
174C23×C113—41no—
175C23×C113—41no—
176C23×C113—41no—
177C23×C113—41no—
178C23×C113—41no—
179C23×C113—41no—
180C23×C113—41no—
181C23×C113#9912yes—
182C23×C113#10212yes—
183C23×C113#10212yes—
184C23×C113#10412yes—
185C23×C113C2×C22⋊C411yescharacteristic
186C23×C113#12112yes—
187C23×C113C2×D811yescharacteristic
188C23×C113C2×SD1611yescharacteristic
189C23×C113#13512yes—
190D4×C113—82no—
191D4×C113—84no—
192D4×C113—84no—
193D4×C113—82no—
194D4×C113—82no—
195C2×C4×C113—24no—
196C2×C4×C113—24no—
197C2×C4×C113—21no—
198C2×C4×C113—21no—
199C2×C4×C113—21no—
200C2×C4×C113—21no—
201C2×C4×C113—21no—
202C2×C4×C113—21no—
203C2×C4×C113—21no—
204C2×C4×C113—21no—
205C2×C4×C113—21no—
206C2×C4×C113—42no—
207C2×C4×C113—42no—
208C2×C4×C113—44no—
209C2×C4×C113—44no—
210C2×C4×C113—44no—
211C2×C4×C113—42no—
212C2×C4×C113—42no—
213C2×C4×C113—44no—
214C2×C4×C113—44no—
215C2×C4×C113—44no—
216C2×C4×C113—41no—
217C2×C4×C113—41no—
218C2×C4×C113—41no—
219C2×C4×C113—41no—
220C2×C4×C113—41no—
221C2×C4×C113—41no—
222C2×C4×C113—41no—
223C2×C4×C113—41no—
224C2×C4×C113—41no—
225C2×C4×C113—82no—
226C2×C4×C113—82no—
227C2×C4×C113—82no—
228C2×C4×C113—82no—
229C2×C4×C113#9912yes—
230C2×C4×C113C4×D412yes—
231C2×C4×C113#12011yescharacteristic
232C2×C4×C113#12311yescharacteristic
233C8×C113—44no—
234C22×C113—22no—
235C22×C113—22no—
236C22×C113—22no—
237C22×C113—22no—
238C22×C113—22no—
239C22×C113—21no—
240C22×C113—21no—
241C22×C113—22no—
242C22×C113—22no—
243C22×C113—22no—
244C22×C113—22no—
245C22×C113—21no—
246C22×C113—22no—
247C22×C113—21no—
248C22×C113—22no—
249C22×C113—22no—
250C22×C113—22no—
251C22×C113—48no—
252C22×C113—48no—
253C22×C113—41no—
254C22×C113—41no—
255C22×C113—41no—
256C22×C113—41no—
257C22×C113—81no—
258C22×C113—81no—
259C22×C113—81no—
260C22×C113—81no—
261C22×C113—81no—
262C22×C113—81no—
263C22×C113—81no—
264C22×C113#32714yescomplemented
265C22×C113#38611yescharacteristic
266C22×C113C2×#9911yescharacteristic
267C22×C113C2×#9911yescharacteristic
268C22×C113C2×#10211yescharacteristic
269C22×C113#41611yescharacteristic
270C22×C113C2×#10411yescharacteristic
271C22×C113#42111yescharacteristic
272C22×C113#46512yes—
273C22×C113#46612yes—
274C4×C113—21no—
275C4×C113—22no—
276C4×C113—21no—
277C4×C113—22no—
278C4×C113—41no—
279C4×C113—84no—
280C4×C113—81no—
281C4×C113—81no—
282C4×C113—81no—
283#9113C11311yesmaximal, characteristic, direct product factor, Sylow
284C2×C113—22no—
285C2×C113—24no—
286C2×C113—22no—
287C2×C113—42no—
288C2×C113—161no—
289C2×C113C2×#32711yescharacteristic
290C2×C113#150111yescharacteristic
291C2×C113#151611yescharacteristic
292C2×C113#151911yescharacteristic
293C2×C113#187111yescharacteristic
294C2×C113#189311yescharacteristic
295C2×C113#189811yescharacteristic
296C22×C22⋊C8C2×C11311yescharacteristic, complemented
297#2847C2×C11311yescharacteristic
298C2×#327C2×C11312yescomplemented
299C22⋊#95C2×C11311yescharacteristic, complemented
300#1294C2×C11312yescomplemented
301C113#911311yescharacteristic, direct product factor, Sylow
302C24×C4C22×C11311yescharacteristic
303C23×C8—21no—
304C2×#121C4×C11311yescharacteristic, complemented
305C2×#121C4×C11311yescharacteristic, complemented
306C2×#121C22×C11311yescharacteristic
307C2×#120—21no—
308C22×C22⋊C4—21no—
309C2×C22⋊C8—21no—
310C2×C22⋊C8—24no—
311C2×C22⋊C8C22×C11312yes—
312#386—21no—
313#386—21no—
314#386—21no—
315#380C4×C11311yescharacteristic, complemented
316#380C4×C11311yescharacteristic, complemented
317#380C22×C11311yescharacteristic
318C2×#95—21no—
319C2×#95C22×C11312yes—
320#327—24no—
321C25D4×C11311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C11311yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C11311yescharacteristic
332C23×C4C2×C4×C11311yescharacteristic
333C23×C4D4×C11311yescharacteristic
334C23×C4D4×C11311yescharacteristic
335C23×C4D4×C11311yescharacteristic
336C23×C4C23×C11311yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C11311yescharacteristic
348C2×C4⋊C4C2×C4×C11311yescharacteristic
349C2×C4⋊C4C2×C4×C11311yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C11314yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C11311yescharacteristic
376C24C22⋊C4×C11311yescharacteristic
377C24D8×C11312yes—
378C24SD16×C11312yes—
379C24C2×D4×C11311yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C11311yescharacteristic
425C22×C4C22⋊C4×C11311yescharacteristic
426C22×C4C22×C4×C11311yescharacteristic
427C22×C4C2×D4×C11311yescharacteristic
428C22×C4C2×D4×C11312yes—
429C22×C4#41×C11312yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C11312yes—
478C23#102×C11312yes—
479C23#102×C11312yes—
480C23#104×C11312yes—
481C23C2×C22⋊C4×C11311yescharacteristic
482C23#121×C11312yes—
483C23C2×D8×C11311yescharacteristic
484C23C2×SD16×C11311yescharacteristic
485C23#135×C11312yes—
486D4—82no—
487D4—84no—
488D4—84no—
489D4—82no—
490D4—82no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C11312yes—
526C2×C4C4×D4×C11312yes—
527C2×C4#120×C11311yescharacteristic
528C2×C4#123×C11311yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—22no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#327×C11314yescomplemented
561C22#386×C11311yescharacteristic
562C22C2×#99×C11311yescharacteristic
563C22C2×#99×C11311yescharacteristic
564C22C2×#102×C11311yescharacteristic
565C22#416×C11311yescharacteristic
566C22C2×#104×C11311yescharacteristic
567C22#421×C11311yescharacteristic
568C22#465×C11312yes—
569C22#466×C11312yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—42no—
583C2—161no—
584C2C2×#327×C11311yescharacteristic
585C2C113×#150111yescharacteristic
586C2C113×#151611yescharacteristic
587C2C113×#151911yescharacteristic
588C2C113×#187111yescharacteristic
589C2C113×#189311yescharacteristic
590C2C113×#189811yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC113×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C24×C4×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C22⋊C8×C113C2semidirect
3. C2×#327×C113C2semidirect
4. C113×C22⋊#95C2semidirect
5. C113×#1294C2semidirect
8. C2×#121×C113C4semidirect
9. C2×#121×C113C4semidirect
19. #380×C113C4semidirect
20. #380×C113C4semidirect
65. C22⋊C8×C113D4semidirect
264. C22×C113#327semidirect
283. #9113C113direct (N × H)
296. C22×C22⋊C8C2×C113semidirect
298. C2×#327C2×C113semidirect
299. C22⋊#95C2×C113semidirect
300. #1294C2×C113semidirect
301. C113#9113direct (N × H)
304. C2×#121C4×C113semidirect
305. C2×#121C4×C113semidirect
315. #380C4×C113semidirect
316. #380C4×C113semidirect
361. C22⋊C8D4×C113semidirect
560. C22#327×C113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C22⋊C8×C1132
C113×#28472
C2×#327×C1132
C113×C22⋊#952
C113×#12942
#9113113